Research On Local Wave Analysis Method And Its Application In The Electrocardiogram Signal Processing

Local wave analysis (LWA) method is a recently developed time-frequency analysismethod, which is based on the local characteristics of the signal itself and thus can besuitable for non-linear and non-stationary signal analysis. Empirical mode decomposition(EMD) is one of the most important techniques of the LWA method. EMD methoddecomposes the complex signal into several basic components called intrinsic modefunctions (IMFs). Combined with the Hilbert transform, the real meaningful instantaneousfrequencies (IF) of the basic components can be calculated. Based on the in-depth studyand summarization to the previous researches, the local wave decomposition methodsrepresented by EMD are studied in this thesis. The main contributions are as follows:Two new envelope fitting methods: the least-length constrained piecewise cubicHermite interpolation (LLC-PCHI) method and the flattest constrained piecewise cubicHermite interpolation method, are proposed. Envelope fitting is one of the important stepsof EMD. It is the key factor that determines EMD’s convergence rate and decompositioncorrectness. In the proposed LLC-PCHI method, taking the length of the fitted envelope asthe target function, Lagrange optimization method is used to optimize the derivatives of theinterpolation nodes. Then the piecewise cubic Hermite interpolation method with theoptimized derivatives is used to fit the more smooth envelopes. The proposed FC-PCHImethod effectively integrates the difference between extremes into the cost function, andapplies a chaos particle swarm optimization method to optimize the derivatives of theinterpolation nodes. The experimental results show that both the two methods caneffectively solve the overshoots and/or undershoots caused by CSI method and theartificial bends caused by piecewise parabola interpolation (PPI) method. Thecorresponding results of EMD can be more reasonable and accurate. Both the two methodscan improve the mode mixing problem well, which is one of the major drawbacks of theoriginal EMD.A new scheme for the choice of parameter δ is proposed, which is based on the least instantaneous period of the signal. An improved partial differential equation based EMD(IPDE-Based EMD) is presented. Sifting process is the crucial part of EMD. It is difficultto study the principles of sifting process due to the loose and vague definition of “localmean”, which is adverse to the EMD’s theoretical framework. The interpolation procedurealways creates additional information that has nothing to do with the original signal. Andthe interpolation makes the sifting and the corresponding IMFs strongly relying on theinterpolants used. Moreover, the interpolation issue can cause the inherent problems duringthe sifting process such as overshoot, undershoot, end issue, etc. An interpolation-free localmean operator is proposed by Diop et al. The establishing scope of local mean operator isfurther promoted in the thesis. The δ IMFproposed by Diop only satisfies the “zerolocal mean” condition of IMF. In the thesis, combined with the properties of the solutionsof the self-adjoint Sturm-Liouville equations, the reason why δ IMFalso satisfies the“exactly one zero between any two successive local extrema” condition of IMF isexpounded, which is not mentioned in Diop’s previous works. A new scheme for the choiceof parameter δ based on the signal’s least instantaneous period is proposed, which makesthe proposed IPDE-Based EMD method be suitable for analysis of unlimited bandwidthsignal. The experimental results show that the proposed PDE-Based EMD can not onlyovercome the end issues caused by interpolations, but also improve the mode mixingproblem compared to the original EMD and the FC-PCHI EMD. Because of the newsignal-based selection of parameter δ, the IPDE-Based EMD is applicable to the unlimitedbandwidth signal analysis.A novel EMD based on regional adaptive hard-threshold filtering algorithm forelectrocardiogram (ECG) signal is proposed. ECG signal is a kind of typical weak andnon-stationary bioelectric signals, which is widely used in the diagnosis and treatment ofmany heart diseases. ECG signal is easily contaminated by severe high frequency noisesuch as electromyographic interference and low frequency noise such as baseline wander.The frequency bands of noise and ECG signal are partially overlapped, which increases thedifficulty of ECG pre-processing. In the thesis, combined with the regional adaptivehard-threshold, the EMD method is applied to ECG pre-processing. The proposed methodcan not only effectively suppress the high frequency noise and low frequency noise butalso better keep the main features of the ECG waveforms.Based on the adaptive property of EMD, a new QRS detector based on the EMD and Hilbert transform and another novel QRS detector based on the IMF’s energy distributionare presented. The QRS complex is the most striking waveform in ECG signal. Accuratedetermination of the QRS complex is crucial in computer-based ECG analysis. Theperformances of the proposed detectors are tested using all48records from MIT-BIHArrhythmia Database. The average correct detection rate is up to99.78%and99.91%respectively, which shows that both the two methods are efficient QRS detectors.